Laplace Transform for Finite Element Analysis of Electromagnetic Interferences in Underground Metallic Structures

Abstract

A numerical methodology is proposed for the calculation of transient electromagnetic interference induced by overhead high-voltage power lines in metallic structures buried in soil—pipelines for oil or gas transportation. A series of 2D finite element simulations was employed to sample the harmonic response of a given geometry section. The numerical inverse Laplace transform of the results allowed obtaining the time domain evolution of the induced voltages and currents in the buried conductors, for any given condition of the power line.

An Efficient Numerical Technique for the Simulation of Charge Transport in Polymeric Dielectrics

“…The right-hand-side of (56) represents the computation that the function f needs to perform. Since the JIT Matlab compiler is not always able to handle loops with complex expressions efficiently [50], [51], the implementation of the function f was extensively vectorized, aiming at reducing computational time. A drawback of using the implicit approach is that the output of the ode23tb function is the state vector at every required time instant.…”

FLARE: A Framework for the Finite Element Simulation of Electromagnetic Interference on Buried Metallic Pipelines

“…This allows one to compute the time-evolution of one of the quantities yielded by the FEM solver, using solutions computed in the complex domain. This formulation is closely related to the quasi-stationary formulation, substituting the purely imaginary jω with the complex variable s. Details of this approach can be found in [31] and are briefly summarized below.…”

“…The main novelties of this work are the vectorized implementation of two solvers for quasi-magnetostatic transient problems, the subsequent comparison and numerical validation of the two approaches, and the benchmarking of three inverse-Laplace routines included in FLARE. The approach based on the inverse-Laplace technique was introduced by the authors in [31]. A similar technique was also recently employed to study quasi-electrostatic problems in [32] and has been applied to other problems in the past, such as unsteady heat flow calculations [33].…”

“…A similar technique was also recently employed to study quasi-electrostatic problems in [32] and has been applied to other problems in the past, such as unsteady heat flow calculations [33]. The work in [31] was focused on the theoretical development of the method, and the developed code was based on a serial Fortran 90 inversion routine by D'Amore et al [34]. In this work, we integrate the approach into the FLARE framework, providing a fully parallelized (shared memory) and more flexible MATLAB ® implementation of the routines.…”

“…We also add two additional (parallel) inversion routines, based on the work of Abate et al [35]; as will be shown in a dedicated section of this work, these techniques are somewhat complementary to that by D'Amore and colleagues, from an accuracy and computational efficiency perspective. With respect to the work in [31], here we want to provide a numerical validation of the inverse-Laplace solution for a transient problem. To do that, we also implement a quasi-magnetostatic solver based on a time-marching procedure, which can operate with either fixed or variable time step lengths; we directly validate the time-marching solution against the solution yielded by the AC/DC module of COMSOL Multiphysics ® on the same problem.…”